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User talk:Cookiefonster/BEAF
I guess you'll start to state in the last section that {X,X,2 (1) 2} = LVO because {X,a (1) 2} is an array with "a" entries (and it can be transfinite) and it corresponds to \theta(\Omega^\alpha,0) . But the same could be done with power towers (it can have transfinite number of terms) and you can reach X^^(X+1) = \varepsilon_\omega . Ikosarakt1 (talk ^ ) 07:51, October 3, 2014 (UTC) :I am aware of the alternate option that's more like Extensible-E, but I specifically said that I want to be as unproblematic as possible and deviate as little as possible from the generally accepted ideas. Cookiefonster (talk) 11:47, October 3, 2014 (UTC) :The problem with having {X,a (1) 2} be an array with "a" entries, where a is transfinite, is that you no longer have an actual writable notation, so rigor goes out the window. We are just guessing that it will be equal to \theta(\Omega^\alpha,0) , but we don't know that, because we don't have an explicit definition for how the notation resolves - and we can't have that, because we don't even have notations for what {X,a (1) 2} resolves to! :The thing is, the (a) separators were clearly intended for the purpose of sending the entry places into the transfinite; that's how it works when the entries are all natural numbers anyway. The (1) separator separates entries of size \omega , the (2) separator separates entries of size \omega^2 , and so on. So we have the capability of representing transfinite entries, we are just choosing not to use it! :So, for the sake of argument, lets use a as a separator to notate the "transfinite" rows. So now we can talk about arrays like {2X, 2X 1 2}, which was a valid array before, we just didn't have a notation for it before. So what does {2X, 2X 1 2} mean? It seems to mean a array with 2X entries of 2X, which would be something like {2X, 2X, 2X, ... 12X, 2X, 2X,...} - which, in addition to being unwritable, it would be a larger array than the original. So there is an issue here that needs to be resolved. Deedlit11 (talk) 12:05, October 3, 2014 (UTC) ::Thanks for the insight, I'm currently developing idea for how to get my Idea to work. Cookiefonster (talk) 22:22, October 3, 2014 (UTC) be sure to specify exactly which OCFs you're using because i die a little every time it isn't done it's vel 19:32, October 6, 2014 (UTC) : RIP many little bits of Vel which have already died * LittlePeng9 (talk) 19:35, October 6, 2014 (UTC) ::i die uniformly it's vel 19:58, October 6, 2014 (UTC) :in the page you use the theta function in both 1- and 2-argument forms, which leads me to assume you're using Bird's theta. except Bird's theta is in fact undefined for θ(Ω^ω) and up. it's vel 19:58, October 6, 2014 (UTC) :::hmmm, i';m a noob, how do would you convert it to other thetas? to me the "official" definitions of the OCFs are all a bunch of mumbo jumbo. Cookiefonster (talk) 20:44, October 6, 2014 (UTC) Continuing BEAF Hmph... Let me get you past that brick wall. {X,X(1)X+1,X,X,...,X,X,X} w/(1)X = {X,X,X,...,X,X,X(1)X,X,X,...,X,X,X} w/X(1)X {X,X,2(1)X+1,X,X,...,X,X,X} w/(1)X = bth member of the sequence: {X,X(1)X+1,X,X,...,X,X,X} w/(1)X, {X,({X,X(1)X+1,X,X,...,X,X,X}w/(1)X)(1)X+1,X,X,...,X,X,X}, etc. Is this a good start? -- A Large Number Googologist -- 21:25, October 21, 2014 (UTC) Have you abandoned this? It's been over a year since you've worked on this before :yes Cookiefonster (talk) 21:19, October 22, 2015 (UTC) Welcome to my world. -- From the googol and beyond -- 22:08, October 22, 2015 (UTC)